The Theory of the Riemann Zeta-function


Author: Late Savilian Professor of Geometry E C Titchmarsh,Titchmarsh, Edward Charles Titchmarsh,Edward Charles Titchmarsh,D. R. Heath-Brown
Publisher: Oxford University Press
ISBN: 9780198533696
Category: Architecture
Page: 412
View: 3902

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The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis.

Exploring the Riemann Zeta Function

190 years from Riemann's Birth
Author: Hugh Montgomery,Ashkan Nikeghbali,Michael Th. Rassias
Publisher: Springer
ISBN: 3319599690
Category: Mathematics
Page: 298
View: 5536

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Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.

Schönheit und Geometrie der Zetafunktion

Beobachtungen und Skizzen
Author: Thomas Kromer
Publisher: BoD – Books on Demand
ISBN: 3842305389
Category: Mathematics
Page: 116
View: 7491

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Die Zeta- und die Etafunktion gehören zu den komplexesten Objekten der Mathematik. In einem strikt geometrischen Ansatz erhalten wir unerwartet schöne Bilder ihres Verlaufs durch die komplexe Zahlenebene, zum Teil verblüffende Zusammenhänge werden in 48 Farbabbildungen illustriert. So können wir nachvollziehen, warum Nullstellen nur für komplexe Zahlen s mit einem Realteil von 0,5 möglich sind. Die Riemannsche Vermutung wird plötzlich plausibel!

Functions of One Complex Variable I


Author: John B. Conway
Publisher: Springer Science & Business Media
ISBN: 9780387903286
Category: Mathematics
Page: 317
View: 2662

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This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - 8 arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

Applications of Random Matrices in Physics


Author: Édouard Brezin,Vladimir Kazakov,Didina Serban,Paul Wiegmann,Anton Zabrodin
Publisher: Springer Science & Business Media
ISBN: 9781402045295
Category: Mathematics
Page: 513
View: 8246

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Proceedings of the NATO Advanced Study Institute on Applications of Random Matrices in Physics, Les Houches, France, 6-25 June 2004

Bulletin

Classe des sciences mathématiques et naturelles. Sciences mathématiques
Author: Srpska akademija nauka i umetnosti
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
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The Mysteries of the Real Prime


Author: M. J. Shai Haran
Publisher: Oxford University Press
ISBN: 9780198508687
Category: Mathematics
Page: 240
View: 4958

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In this important and original monograph, useful for both academic and professional researchers and students of mathematics and physics, the author describes his work on the Riemann zeta function and its adelic interpretation. It provides an original point of view, bringing new, highly useful dictionaries between different fields of mathematics. It develops an arithmetical approach to the continuum of real numbers and unifies many areas of mathematics including: Markov Chains, q-series, Elliptic curves, the Heisenberg group, quantum groups, and special functions (such as the Gamma, Beta, Zeta, theta, Bessel functions, the Askey-Wilson and the classical orthagonal polynomials) The text discusses real numbers from a p-adic point of view, first mooted by Araeklov. It includes original work on coherent theory, with implications for number theory and uses ideas from probability theory including Markov chains and noncommutative geometry which unifies the p-adic theory and the real theory by constructing a theory of quantum orthagonal polynomials.

CMFT


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Geometric function theory
Page: N.A
View: 7668

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Actas


Author: Antonio A. R. Monteiro
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
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Combinatorics


Author: Russell Merris
Publisher: Brooks/Cole Publishing Company
ISBN: N.A
Category: Mathematics
Page: 367
View: 3509

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Reviews in Number Theory, 1984-96

As Printed in Mathematical Reviews
Author: N.A
Publisher: Amer Mathematical Society
ISBN: 9780821809372
Category: Mathematics
Page: 1012
View: 5404

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These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.

Mathematics for the General Reader


Author: E.C. Titchmarsh
Publisher: Courier Dover Publications
ISBN: 0486821188
Category: Mathematics
Page: 192
View: 9495

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"A first-class mathematician's lucid, unhurried account of the science of numbers from arithmetic through the calculus." — James R. Newman, The World of Mathematics. This highly accessible introduction to mathematics is geared toward readers seeking a firm grasp of the essentials of mathematical theory and practice. The treatment also offers a concise outline of mathematical history and a clearer notion of why mathematicians do what they do. Author E. C. Titchmarsh, who served for many years as Savilian Professor of Geometry at Oxford University, begins with counting and the fundamentals of arithmetic. He guides readers through the complexities of algebra, fractions, geometry, irrational numbers, logarithms, infinite series, complex numbers, quadratic equations, trigonometry, functions, and integral and differential calculus. Titchmarsh's graceful, fluid style helps make complicated topics easier to grasp, and his inclusion of numerous examples will prove especially helpful to readers with little or no background in mathematics.